IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v23y2012i2d10.1007_s10878-010-9347-1.html
   My bibliography  Save this article

Packing cycles exactly in polynomial time

Author

Listed:
  • Qin Chen

    (University of Hong Kong)

  • Xujin Chen

    (Chinese Academy of Sciences)

Abstract

Let G=(V,E) be an undirected graph in which every vertex v∈V is assigned a nonnegative integer w(v). A w-packing is a collection of cycles (repetition allowed) in G such that every v∈V is contained at most w(v) times by the members of . Let 〈w〉=2|V|+∑ v∈V ⌈log (w(v)+1)⌉ denote the binary encoding length (input size) of the vector (w(v): v∈V) T . We present an efficient algorithm which finds in O(|V|8〈w〉2+|V|14) time a w-packing of maximum cardinality in G provided packing and covering cycles in G satisfy the ℤ+-max-flow min-cut property.

Suggested Citation

  • Qin Chen & Xujin Chen, 2012. "Packing cycles exactly in polynomial time," Journal of Combinatorial Optimization, Springer, vol. 23(2), pages 167-188, February.
    • Handle: RePEc:spr:jcomop:v:23:y:2012:i:2:d:10.1007_s10878-010-9347-1
    DOI: 10.1007/s10878-010-9347-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-010-9347-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-010-9347-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. EDMONDS, Jack & GILES, Rick, 1977. "A min-max relation for submodular functions on graphs," LIDAM Reprints CORE 301, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. András Frank, 2005. "On Kuhn's Hungarian Method—A tribute from Hungary," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(1), pages 2-5, February.
    2. Xujin Chen & Guoli Ding & Xiaodong Hu & Wenan Zang, 2006. "A Min-Max Relation on Packing Feedback Vertex Sets," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 777-788, November.
    3. Alexandre Skoda, 2019. "Convexity of graph-restricted games induced by minimum partitions," Post-Print halshs-01617023, HAL.
    4. Meijia Han & Wenxing Zhu, 2023. "Nonnegative partial s-goodness for the equivalence of a 0-1 linear program to weighted linear programming," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-37, July.
    5. Mao-Cheng Cai & Xiaoguang Yang & Yanjun Li, 1999. "Inverse Polymatroidal Flow Problem," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 115-126, July.
    6. Aardal, K. & van Hoesel, C.P.M., 1995. "Polyhedral techniques in combinatorial optimization," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    7. Alexandre Skoda, 2017. "Inheritance of Convexity for the P min-Restricted Game," Post-Print halshs-01660670, HAL.
    8. Alexander Bockmayr & Friedrich Eisenbrand, 2001. "Cutting Planes and the Elementary Closure in Fixed Dimension," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 304-312, May.
    9. Alexandre Skoda, 2016. "Complexity of inheritance of F-convexity for restricted games induced by minimum partitions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01382502, HAL.
    10. Xujin Chen & Guoli Ding & Wenan Zang, 2008. "A Characterization of Box-Mengerian Matroid Ports," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 497-512, May.
    11. Alexandre Skoda, 2016. "Complexity of inheritance of F-convexity for restricted games induced by minimum partitions," Post-Print halshs-01382502, HAL.
    12. Guoli Ding & Lei Tan & Wenan Zang, 2018. "When Is the Matching Polytope Box-Totally Dual Integral?," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 64-99, February.
    13. Kristóf Bérczi & András Frank, 2018. "Supermodularity in Unweighted Graph Optimization I: Branchings and Matchings," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 726-753, August.
    14. Alexandre Skoda, 2017. "Inheritance of Convexity for the Pmin-Restricted Game," Documents de travail du Centre d'Economie de la Sorbonne 17051, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    15. Qin Chen & Xujin Chen & Wenan Zang, 2016. "A Polyhedral Description of Kernels," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 969-990, August.
    16. Alexandre Skoda, 2016. "Inheritance of Convexity for Partition Restricted Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01318105, HAL.
    17. Aardal, K.I. & van Hoesel, S., 1995. "Polyhedral Techniques in Combinatorial Optimization," Discussion Paper 1995-57, Tilburg University, Center for Economic Research.
    18. Xujin Chen & Zhibin Chen & Wenan Zang, 2010. "A Unified Approach to Box-Mengerian Hypergraphs," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 655-668, August.
    19. Alexandre Skoda, 2019. "Convexity of graph-restricted games induced by minimum partitions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01617023, HAL.
    20. Alexandre Skoda, 2016. "Complexity of inheritance of F-convexity for restricted games induced by minimum partitions," Documents de travail du Centre d'Economie de la Sorbonne 16055, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:23:y:2012:i:2:d:10.1007_s10878-010-9347-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.